Related papers: An energy-based coupling approach to nonlocal inte…

We study the systematic numerical approximation of a class of Allen-Cahn type problems modeling the motion of phase interfaces. The common feature of these models is an underlying gradient flow structure which gives rise to a decay of an…

This paper proposes a deep unfitted Nitsche method for computing elliptic interface problems with high contrasts in high dimensions. To capture discontinuities of the solution caused by interfaces, we reformulate the problem as an energy…

We consider an interface problem often arising in transport problems: a coupled system of partial differential equations with one (elliptic) transport equation on a bounded domain and one equation (in this case the Laplace problem) on the…

Damping of structures and systems is often dominated by frictional dissipation in connections, the prediction of which remains a longstanding scientific challenge. Previous studies have shown that the actual topography of contact interfaces…

There are various methods for modeling phase transformations in materials science, including general classes of phase-field methods and reactive diffusion methodologies, which most importantly differ in their treatment of interface energy.…

A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is also…

We provide a review of recent advancements in nonlocal continuous models for migration, mainly from the perspective of its involvement in embryonal development and cancer invasion. Particular emphasis is placed on spatial nonlocality…

Cosmological models involving an interaction between dark matter and dark energy have been proposed in order to solve the so-called coincidence problem. Different forms of coupling have been studied, but there have been claims that…

Nanoscale design of surfaces and interfaces is essential for modern technologies like organic LEDs, batteries, fuel cells, superlubricating surfaces, and heterogeneous catalysis. However, these systems often exhibit complex surface…

In this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be…

This article reviews a new and general theory of nonuniform fluids that naturally incorporates molecular scale information into the classical van der Waals theory of slowly varying interfaces. The method optimally combines two standard…

This article presents a multi-physics methodology for the numerical simulation of physical systems that involve the non-linear interaction of multi-phase reactive fluids and elastoplastic solids, inducing high strain-rates and high…

We present a new formulation based on the classical Dirichlet-Neumann formulation for interface coupling problems in linearized elasticity. By using Taylor series expansions, we derive a new set of interface conditions that allow our…

We explore the possibility of modifying the classical Gauss free energy functional used in capillarity theory by considering surface tension energies of nonlocal type. The corresponding variational principles lead to new equilibrium…

Multi-component fluid flow simulations in multi-scale porous structures often involve regions that are under-resolved at practical computational resolutions. Accurately capturing the contributions from these unresolved regions is critical.…

In this work, we study one-dimensional nonlocal elliptic transmission problems with piecewise constant coefficients that may change sign across an interface. In the local setting, we recall the T-coercive structure of the problem and…

We map molecular dynamics simulations of fluid-fluid interfaces onto mesoscale continuum theories for partially miscible fluids. Unlike most previous work, we examine not only the interface order parameter and density profiles, but also the…

We consider a model for the evolution of an interface in a heterogeneous environment governed by a parabolic equation. The heterogeneity is introduced as obstacles exerting a localized dry friction. Our main result establishes the emergence…

We investigate the impact of limited data on training pairwise energy-based models for inverse problems aimed at identifying interaction networks. Utilizing the Gaussian model as testbed, we dissect training trajectories across the…

We consider a class of nonconvex energy functionals that lies in the framework of the peridynamics model of continuum mechanics. The energy densities are functions of a nonlocal strain that describes deformation based on pairwise…